The great distance in space and time between activities occurring at the atomic and cellular levels makes it difficult to include atomistic and molecular information into models of cellular behavior. This challenge is addressed by multiscale or multi-resolution approaches that use coarse-grained models and molecular dynamics (MD) in distinct regions of the cell. The accuracy and characteristics of the coarse-grained model, which roughly represents the complete MD description, determine their usefulness. We introduce a series of very low-dimensional stochastic coarse-grained (SCG) models expressed as nonlinear stochastic differential equations. The non Gaussian force distribution shown in MD simulations and incomprehensible for linear models is included into the nonlinear SCG model. It is shown that the nonlinearities may be selected so as to avoid adding to the difficulty of the SCG description's parametrization using in depth MD simulations. Gamma functions are used to express the SCG model's solution